Magdalini’s name day is July 22, the feast of Mary Magdalene.
Churches that follow the Old (Julian) Calendar keep the same feast on August 4 of the civil calendar. See everything commemorated on July 22.
The saint behind the name

Mary Magdalene
July 22, Holy Woman, Μαρία Μαγδαληνή
St. Mary Magdalene, the Myrrh-Bearer and Equal-to-the-Apostles, was healed by the Lord of seven demons and thereafter followed Him from Galilee, ministering to Him from her own means. She stood by the Cross when most had fled, and coming early to the tomb she was among the first to behold the risen Christ, who sent her to announce the Resurrection to the Apostles.
Also celebrating on July 22
These names share the feast, many of them other forms of the same name:
What to say on a name day
The Greek wish is Χρόνια Πολλά (Chronia Polla), “many years.” A call or a short message on the day is what people remember. See name day wishes you can send and what a name day is.